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A239740 a(n) = gcd(Sum_{k=1...n} F(k), Product{j=1...n} F(j)), where F(k) is the k-th Fibonacci number. 2
1, 1, 2, 1, 6, 20, 3, 18, 8, 143, 8, 8, 21, 986, 84, 63, 220, 6764, 55, 770, 144, 46367, 144, 432, 377, 317810, 16588, 377, 43428, 2178308, 987, 53298, 2584, 14930351, 2584, 18088, 6765, 102334154, 784740, 20295, 2054476, 701408732, 17711, 1664834, 46368 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,3
COMMENTS
The Fibonacci numbers in the sequence are 1, 2, 3, 8, 21, 55, 144, 377, 987, ... and a majority are elements of A001906 (F(2*n)= bisection of Fibonacci sequence).
We find consecutive values such that (1, 2), (2, 3), (20, 21), (986, 987), (6764, 6765), (46367, 46368), (317810, 317811), (14930351, 14930352), ...
LINKS
EXAMPLE
The first 8 Fibonacci numbers are 1,1,2,3,5,8,13,21 and 1+1+2+3+5+8+13+21 = 54. So a(8) = gcd(54, 1*1*2*3*5*8*13*21) = 18.
MAPLE
with(combinat, fibonacci):seq(gcd(add(fibonacci(i), i=1..n), mul(fibonacci(j), j=1..n)), n=1..60);
MATHEMATICA
nn=60; With[{prs=Fibonacci[Range[nn]]}, Table[GCD[Total[Take[prs, n]], Times@@Take[ prs, n]], {n, nn}]]
PROG
(Haskell)
a239740 n = gcd (sum fs) (product fs)
where fs = take n $ tail a000045_list
-- Reinhard Zumkeller, Mar 27 2014
CROSSREFS
Sequence in context: A101032 A025271 A153804 * A268371 A318918 A100404
KEYWORD
nonn
AUTHOR
Michel Lagneau, Mar 26 2014
STATUS
approved

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Last modified June 9 12:36 EDT 2023. Contains 363178 sequences. (Running on oeis4.)